FearlessSymmetry

Fearless Symmetry

  • Not bad. Good attempt to explain cutting edge math.
  • Tough going in the end, probably could have been done better.
  • Mathematical definitions create usage, not describe it.
  • Mathematical definitions cannot be wrong, only inconsistent or useless.
  • Lie group theory a marriage between calculus and group theory
  • Complex numbers forced on the world when solving CUBIC equiations. (Assumed x2 + 1 = 0 had no solutions) Intermediate steps of the cubic equation involve imaginary numbers even though the final solutions are real.
  • Every root of a complex equation is already in C.
  • "2x3xR=C" the bible, ie "pi = 3" the bible.
  • There is no (cannot be) a general method for finding all integer solutions to all systems of Z-equations in many variables
  • Pi is not in Q-Alg, this fact is apparently very hard to prove.
  • Not every number in Q-Alg can be obtained from the integers with repeated application of +,-,*,/ and ()(1/n).
  • There is only one element of G (The absolute Galois Group) other than the identity which we can give a complete discription: complex conjugation.
  • A representation that is not faithful emphasizes certiant features of the sourse group and obscures others, enabling us to better understand the source group.
  • Some very large and complicated groups have been shown to be isomorphic to the Galois group of a poly-nominal (Including the Monster group)
  • Open conjectures: Poincare, Riemann Hypothesis, P==NP
  • Proving things about poly-nominals usual much easier than proving things about integers: Poly-Nominals have roots and can be differentiated. (Is there a notion of differentiation that can be applied to integers? Primes? )

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